A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.00$, and bags of cookies cost $$4.50$, and sales equaled $$63.50$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8x+4.5y = 63.5}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${8x + 4.5}{(x+3)}{= 63.5}$ Simplify and solve for $x$ $ 8x+4.5x + 13.5 = 63.5 $ $ 12.5x+13.5 = 63.5 $ $ 12.5x = 50 $ $ x = \dfrac{50}{12.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(4)}{ + 3}$ ${y = 7}$ You can also plug ${x = 4}$ into $ {8x+4.5y = 63.5}$ and get the same answer for $y$ ${8}{(4)}{ + 4.5y = 63.5}$ ${y = 7}$ $4$ bags of candy and $7$ bags of cookies were sold.